The Bhattacharyya coefficient of two discrete probability distributions is defined as $$ BC(p,q) = \sum_{i=1}^n \sqrt{p_iq_i}. $$ This coefficient lies within the interval $[0,1]$ and if $p=q$ then it is 1 as $$ \sum_{i=1}^n \sqrt{p_i^2} = \sum_{i=1}^n p_i = 1. $$ Thus values lower than 1 might indicate that $p$ and $q$ differ. Are there any thresholds derived in the literature or significance tests that give guidance when we can accept the hypothesis that $p$ and $q$ differ? Login To add answer/comment